Posted by Miley on .
can someone please show me step by step how to do this problem...
1/2log base 4 252(3logbase4 5log base 4 25)

alg 2. 
Damon,
.5 log4 5^2 = log4(5)
2(3 log4 5  2 log4 5 ) = 2 log4 5
so we have
1 log4(5)
= log4(.2)
that might be the answer you are looking for but if you need a number
4^x = .2 ?
x ln 4 = ln .2
x = 1.39/1.61
=  .863 
alg 2. 
Miley,
I have to condense it... thanks for your help

alg 2. 
Reiny,
1/2log base 4 252(3logbase4 5log base 4 25)
= 1/2 log_{4} 25  2(3log_{4} 5  log_{4} 25)
= log_{4}5  2(log_{4}125  log_{4}25)
= log_{4}5  2(log_{4}(125/25)
= log_{4}5  2log_{4}5
= log_{4}5 
alg 2. 
Miley,
my teacher has a different answer... she has log base 4(1/25).

alg 2. 
Damon,
Well, I think log4 (1/5)
I got 1 log4 5
she got 2 log4 5
one of us subtracted wrong or something
However Reiny and I agree exactly, so the odds are in our favor : 
alg 2. 
Miley,
my teacher got log base 4 (1/125) and it's a quiz review sheet, and all the math teachers look over it... sooo... I get how to simplify the 1/2 part but how do i condense the parenthesies

alg 2. 
Reiny,
Well, Miley, if you typed your question correctly, then your teacher is wrong.
Even though both Damon and I did it slightly differently, we came up with the same answer.
I evaluated your original expression the way it stands on my calculator, and got the same result as our answer at the end. 
alg 2. 
Damon,
By the way, your teacher and I both said
n log4 x = log4 x^n = log4 (1/x^n)
which is how we converted the negative log to positive 
alg 2. 
Miley,
can you please show me how to condense 2(3logbase 4 5log base 4 5), thanks:)

alg 2. 
Reiny,
OK, Miley, in your first post you had
...2(3logbase4 5log base 4 25)
and now you typed
...2(3logbase4 5log base 4 5)
GheeeeZZ!!!! 
alg 2. 
Miley,
Sorry it's not like i did that on purpose! Take a CHILL PILL!

alg 2. 
Damon,
I do not know what to say. Reiny and I did the parentheses quite different ways and both got the same answer.

alg 2. 
Miley,
Can you please break it down step by step and show me how you did it! thanks:)

alg 2. 
Damon,
You have two ways to condense the inside the parentheses up there
I did it by saying log 25 = 2 log 5
Reiny did it by saying
log 125  log 25 = log (125/25) = log 5 
alg 2. 
Miley,
what happen to the base 4?

alg 2. 
Damon,
What I wrote a few minutes ago is true for any old base so I left the 4 out

alg 2. 
Miley,
ohh okay thanks

alg 2. 
Damon,
2(3logbase 4 5log base 4 5)
Hey, that is not what you wrote in the original question
that is just 2 (2 log4 5)
which is
4 log4 of 5
NOW
log4 5  4 log4 5
= 3 log4 5
= log4 (1/5^3)
= log4 (1/125) 
alg 2. 
Miley,
oh my bad, sorry. wait how did you get rid of the negative two on the outside?

alg 2. 
Damon,
2(2 log) = 4 log

alg 2. 
Miley,
huh??

alg 2. 
aleah,
Uh...I'm posting this one on gothomework.tk